Alan Macnaughton

Tipping and the Mcquatters Formula

The Internal Revenue Service has been attempting to reduce tax evasion on tips paid in cash by imputing this income on the basis of credit card tip income. This note points out that the effective marginal tax rate on a credit card tip can as a result be very high, possibly in excess of 100%. This rate may affect behavior and could detract from the social acceptability of the imputation formula.

Discovering inequality conditions in the analytic solution of optimization problems

Necessary and sufficient conditions for the problem of maximizing or minimizing a function subject to inequality constraints are given by a set of equalities and inequalities known as the Kuhn-Tucker conditions. These conditions can provide an analytic solution to the optimization problem if the artificial variables known as Lagrange multipliers can be eliminated. However, this is tedious to do by hand. This paper develops a computer program to assist in the solution process which combines symbolic computation and automated reasoning techniques. The program may also be useful for other problems involving algebraic reasoning with inequalities which employ general functions or symbolic parameters.

Discovering inequality conditions in the analytical solution of optimization problems

The Kuhn-Tucker conditions can provide an analytic solution to the problem of maximizing or minimizing a function subject to inequality constraints, if the artificial variables known as Lagrange multipliers can be eliminated. This paper describes an automated reasoning program that assists in the solution process. The program may also be useful for other problems involving algebraic reasoning with inequalities.